KKR & Co. pumped $1.2 billion into First Data Corp., an unusual move showing that its debt-fueled takeover of the payment processor seven years ago remains a burden for the buyout firm.

Credit-card processor First Data has been in the red since KKR took it over in 2007 for roughly $26 billion in one of the largest-ever private-equity buyouts. For a while, KKR refinanced First Data's hefty debt load to ease pressure on the company. Now, it is injecting equity as part of a $3.5 billion investment that includes $2...